Resolution lower bounds for the weak functional pigeonhole principle

Authors:
Alexander A. Razborov
Affiliations:
Steklov Mathematical Institute, Moscow, Russia and Institute for Advanced Study, Princeton
Venue:
Theoretical Computer Science - Logic and complexity in computer science
Year:
2003

Citing 13
Cited 7

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Abstract

We show that every resolution proof of the functional version FPHPnm of the pigeonhole principle (in which one pigeon may not split between several holes) must have size exp(Ω(n/(log m)2)). This implies an exp(Ω(n1/3)) bound when the number of pigeons m is arbitrary.